Terahertz time domain spectroscopy of ordered and disordered half-doped manganites

Terahertz (THz) time domain spectroscopic studies were carried on Nd$_{0.5}$Ca$_{0.5}$MnO$_{3}$ and Nd$_{0.5}$Ca$_{0.48}$Ba$_{0.02}$MnO$_{3}$ (NCBMO) charge-ordered (CO) manganite thin films. Temperature dependent complex optical conductivity ($\tilde {\sigma }=\sigma _1 +i\sigma _2 )$ was studied to probe the cation disorder effects on low energy charge dynamics. The frequency dependent $\sigma _{1}$ suggests formation of charge-density-waves in these manganites. A doping induced cation disorder, as in the case of NCBMO, weakens the CO state.$^{1}$ However, at THz frequency, there are subtle effects of disorder on $\tilde {\sigma }$of NCBMO in a definite low temperature range. As temperature increases to 150 K (N\'{e}el temperature), changes are observed on the trends of temperature dependent dielectric constant ($\varepsilon _{1})$ and $\sigma _{1}$. The Ba doping effects are dominant above the charge-ordering transition temperature. The \textit{$\varepsilon $}$_{1}$ and \textit{$\sigma $}$_{1}$, both increase with temperature and show a scaling relationship, \textit{$\varepsilon $}$_{1~\propto }\sigma _{1}$, that is consistent with similar result observed for (PrCaSr)MnO$_{3}$ manganite.$^{2}$ $^{1}$Mavani \textit{et al.}, Europhys. Lett. (in print). $^{2}$Pimenove \textit{et al.}, Phys. Rev. B 73,220407(R).